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# When a cylindrical tank is filled with water at a rate of 22

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When a cylindrical tank is filled with water at a rate of 22 [#permalink]

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18 Dec 2005, 02:16
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When a cylindrical tank is filled with water at a rate of 22 cubic meters per hour, the level of water in the tank rises at a rate of 0.7 meters per hour. Which of the following best approximates the radius of the tank in meters?

A. √10/2
B. √10
C. 4
D. 5
E. 10

OPEN DISCUSSION OF THIS QUESTION IS HERE: when-a-cylindrical-tank-is-filled-with-water-at-a-rate-of-160344.html
[Reveal] Spoiler: OA

Last edited by Bunuel on 19 Aug 2014, 02:27, edited 1 time in total.
Renamed the topic, edited the question and added the OA.
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Re: When a cylindrical tank is filled with water at a rate of 22 [#permalink]

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18 Dec 2005, 02:26
In 1 hr,

volume = 22 = pi (r^3)(0.7)

pi is 22/7 (approximately), so 22 = 22/7(r^3)(7/10)

22 = 22/10(r^3)
10 = r^3

So choice c,d, and e are out since 4^3, 5^3 and 10^3 are out greater than 10.

sqrt9 = 3, sqrt 16 = 4, so sqrt10 is going to be slightly above 3. So choice B is out, since r^3 = 10 * sqrt(10) which is going to be slightly above 30.

I pick A
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Re: When a cylindrical tank is filled with water at a rate of 22 [#permalink]

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18 Dec 2005, 03:00
My choice too, but we are both wrong. MGMAT ranks this as a 600 level Q problem.
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Re: When a cylindrical tank is filled with water at a rate of 22 [#permalink]

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18 Dec 2005, 05:10
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Hello, I choose B, since

the amount of water that flows into the cyclindrical tank can be expressed as

22= 0,7 * rÂ²* Pi, thus

220/7= rÂ²* Pi, which is approx.

210/7=30= rÂ²* Pi, since Pi equals 3,14 and 220 is slghtly above 30 we can estimate that

rÂ²= 10,

which is B
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Re: When a cylindrical tank is filled with water at a rate of 22 [#permalink]

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18 Dec 2005, 09:43
Another vote for B. allabout's explanation is very clear.
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Re: When a cylindrical tank is filled with water at a rate of 22 [#permalink]

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18 Dec 2005, 21:40
I made an error in calculation !! Sorry, the volume of the cylinder should be pi*r^2*h. I do not know why I put it down as pi*r^3^h and even went on to work out the problem.
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Re: When a cylindrical tank is filled with water at a rate of 22 [#permalink]

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18 Dec 2005, 21:43
Here's my re-worked solution:

volume = 22 = pi (r^2)(0.7)

22 = 22/7 (7/10)(r^2)
10 = r^2
r = sqrt(10)

Ans: B
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Re: When a cylindrical tank is filled with water at a rate of 22 [#permalink]

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18 Dec 2005, 23:36
GMATT73 wrote:
When a cylindrical tank is filled with water at a rate of 22 cubic meters per hour, the level of water in the tank rises at a rate of 0.7 meters per hour. Which of the following best approximates the radius of the tank in meters?

A. sqrt10/2
B. sqrt10
C. 4
D. 5
E. 10

22 = PI r^2 * 0.7
22 = 22/7 * r^2 * 0.7
1= r^2/10
=> r= Sqrt(10) ----> B
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Re: When a cylindrical tank is filled with water at a rate of 22 [#permalink]

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20 Dec 2005, 00:09
Yes, the trick to this problem is remembering that pi=22/7.

OA is B.
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Re: When a cylindrical tank is filled with water at a rate of 22 [#permalink]

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20 Dec 2005, 15:33
obviously B

22 CM =Pi* r^2*h (balancing the volume)

22 CM = Pi*r^2*0.7

r= sqrt (22/0.7)*1/Pi BTW 22/7 = pi

r= sqrt10
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Re: When a cylindrical tank is filled with water at a rate of 22 [#permalink]

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20 Dec 2005, 20:03
GMATT73 wrote:
My choice too, but we are both wrong. MGMAT ranks this as a 600 level Q problem.

I got B so I am a 600 level person.
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Re: When a cylindrical tank is filled with water at a rate of 22 [#permalink]

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20 Dec 2005, 20:08
Bhai wrote:
GMATT73 wrote:
My choice too, but we are both wrong. MGMAT ranks this as a 600 level Q problem.

I got B so I am a 600 level person.

Since the OA is B, and you've answered B, it means you're too good for 600 level questions, nothing to be sad about yeah?
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Re: When a cylindrical tank is filled with water at a rate of 22 [#permalink]

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18 Aug 2014, 21:28
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Re: When a cylindrical tank is filled with water at a rate of 22 [#permalink]

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18 Aug 2014, 22:20
GMATT73 wrote:
When a cylindrical tank is filled with water at a rate of 22 cubic meters per hour, the level of water in the tank rises at a rate of 0.7 meters per hour. Which of the following best approximates the radius of the tank in meters?

A. sqrt10/2
B. sqrt10
C. 4
D. 5
E. 10

The area of the base = 22/0.7 = 220/7 = about 31 m^2 = Pi * r^2
--> r^2 = 31/3.14 = about 10
--> r = sqrt (10)

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Re: When a cylindrical tank is filled with water at a rate of 22 [#permalink]

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19 Aug 2014, 02:28
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GMATT73 wrote:
When a cylindrical tank is filled with water at a rate of 22 cubic meters per hour, the level of water in the tank rises at a rate of 0.7 meters per hour. Which of the following best approximates the radius of the tank in meters?

A. √10/2
B. √10
C. 4
D. 5
E. 10

We are basically told that a cylinder with a height of 0.7 (7/10) meters has the volume of 22 cubic meters.

$$volume_{cylinder}=\pi{r^2}h=22$$ --> $$\pi{\approx{\frac{22}{7}}}$$ --> $$\frac{22}{7}*r^2*\frac{7}{10}=22$$ --> $$r=\sqrt{10}$$.

OPEN DISCUSSION OF THIS QUESTION IS HERE: when-a-cylindrical-tank-is-filled-with-water-at-a-rate-of-160344.html
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Re: When a cylindrical tank is filled with water at a rate of 22   [#permalink] 19 Aug 2014, 02:28
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# When a cylindrical tank is filled with water at a rate of 22

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